Аннотация:
The notion of discriminantly separable polynomials of degree two in each of three variables has been recently introduced and related to a class of integrable dynamical systems.
Explicit integration of such systems can be performed in a way similar to Kowalevski's original integration of the Kowalevski top.
Here we present the role of discriminantly separable polynomials in integration of yet another well known integrable system, the so-called generalized Kowalevski top — the motion of a heavy rigid body about a fixed point in a double constant field.
We present a novel way to obtain the separation variables for this system, based on the discriminantly separable polynomials.
The research was partially supported by the Serbian Ministry of Science and Technological Development, Project 174020 Geometry and Topology of Manifolds, Classical Mechanics and Integrable Dynamical Systems.
Поступила в редакцию: 26.09.2017 Исправленный вариант: 15.11.2017
Образец цитирования:
Vladimir Dragovich, Katarina Kukić, “Discriminantly separable polynomials and the generalized Kowalevski top”, Theor. Appl. Mech., 44:2 (2017), 229–236
\RBibitem{DraKuk17}
\by Vladimir~Dragovich, Katarina~Kuki{\'c}
\paper Discriminantly separable polynomials and the generalized Kowalevski top
\jour Theor. Appl. Mech.
\yr 2017
\vol 44
\issue 2
\pages 229--236
\mathnet{http://mi.mathnet.ru/tam31}
\crossref{https://doi.org/10.2298/TAM170926016D}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000423915600008}
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/tam31
https://www.mathnet.ru/rus/tam/v44/i2/p229
Эта публикация цитируется в следующих 3 статьяx:
Vladimir Yu OL'SHANSKII, “Regular precession of a rigid body in two uniform fields”, Mechanics Research Communications, 127 (2023), 104041
Anani Komla Adabrah, Vladimir Dragović, Milena Radnović, “Periodic Billiards Within Conics in the Minkowski Plane and Akhiezer Polynomials”, Regul. Chaotic Dyn., 24:5 (2019), 464–501
Vladimir Dragović, Milena Radnović, “Caustics of Poncelet Polygons and Classical Extremal Polynomials”, Regul. Chaotic Dyn., 24:1 (2019), 1–35
Цитирование в формате AMSBIB
Обратная связь: